# What is the torque from this force?

Computes torque from a force, the lever arm and the angle between them (τ = rF sin θ), or the force or lever arm for a torque, in N·m, lb·ft and lb·in.

- Page: https://www.acalculator.org/physics/torque-calculator
- JSON spec: https://www.acalculator.org/physics/torque-calculator.json
- Version: 48ea3703dff7

## Default answer

Example with the default inputs (Find Torque, Force (F) 50 lbf, Lever arm (r) 12 in, Torque unit lb·ft, Angle (θ, degrees) 90): The torque is 50 lb·ft.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which value to work out from the other two. |
| f | Force (F) | The push or pull on the lever, such as your hand on a wrench. |
| r | Lever arm (r) | The distance from the axis of turning (the bolt) to where the force pushes. |
| t | Torque (τ) | The torque you need, in the torque unit below. |
| u | Torque unit | Newton-metres, pound-feet or pound-inches. |
| a | Angle (θ, degrees) | The angle between the lever arm and the force, in degrees; 90 when you push straight across. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| answer | Answer | The value you asked for, in the unit named in the answer. |
| shownUnit | Answer unit | The unit of the answer. |
| what | Answer is | What the answer measures: torque, force or lever arm. |
| nm | Torque (N·m) | The torque in newton-metres. |
| lbft | Torque (lb·ft) | The torque in pound-feet. |
| lbin | Torque (lb·in) | The torque in pound-inches. |
| newtons | Force (N) | The force in newtons. |
| pounds | Force (lbf) | The force in pounds-force. |
| meters | Lever arm (m) | The lever arm in metres. |
| feet | Lever arm (ft) | The lever arm in feet. |
| perpendicular | Perpendicular lever arm r⊥ (m) | r sin θ: the part of the lever arm square to the force, in metres. |

## Method

τ = r × F × sin θ; F = τ ÷ (r sin θ); r = τ ÷ (F sin θ).

## Assumptions

- θ is the angle between the lever arm (from the axis to where the force acts) and the force, from 0° to 180°.
- The answer is the size of the torque; its direction (clockwise or counterclockwise) is not shown.
- 1 lb·ft = 1 lbf × 1 ft = 0.3048 × 4.4482216152605 N·m (NIST SP 811).

## Worked examples

1. find = torque, f = 40, r = 4, a = 90, u = nm gives answer = 160, nm = 160. Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.14 (40 N at 4 m and 90° gives 160 N·m).
2. find = torque, f = 20, r = 0.5, a = 150, u = nm gives answer = 5, perpendicular = 0.25. Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.15 (20 N at r = 0.5 m and 150° gives 5.0 N·m).
3. find = torque, f = 44.482216, r = 0.6096, a = 90, u = lbft gives answer = 20, lbft = 20, lbin = 240, nm = 27.116359. Source: NIST SP 811 (2008), Appendix B.8 (1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8.
4. find = force, t = 80, r = 0.4572, a = 90, u = lbft gives answer = 53.333333, pounds = 53.333333. Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque.
5. find = arm, t = 120, f = 400, a = 30, u = nm gives answer = 0.6, meters = 0.6. Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque.

## FAQ

### How do I calculate torque?

Multiply the lever arm by the force and by the sine of the angle between them: τ = rF sin θ. Pushing 40 N square to a 4 m arm gives 4 × 40 × sin 90° = 160 N·m.

### What is the lever arm?

The lever arm r is the distance from the axis of turning (the bolt or hinge) to the point where the force pushes. The part of it square to the force, r sin θ, is the perpendicular lever arm r⊥, and τ = r⊥F.

### Why does the angle matter?

Only the part of the force square to the arm turns it. At 90° all of it counts (sin 90° = 1); at 30° half of it counts (sin 30° = 0.5); at 0° or 180° the force points along the arm and makes no torque.

### How much force do I need on a wrench?

Divide the torque by the lever arm: F = τ ÷ (r sin θ). For 80 lb·ft on an 18 in (1.5 ft) bar pushed square to it, you need 80 ÷ 1.5 = 53.3 lbf.

### How do I convert lb·ft to N·m?

One pound-foot is 1 lbf × 1 ft = 4.4482216152605 N × 0.3048 m = 1.3558 N·m. So 20 lb·ft is 27.12 N·m, and 20 lb·ft is 240 lb·in.

### Is torque the same as work?

Both can be written in N·m, but they are different. Work is a force times a distance moved along it; torque is a force times a lever arm square to it, and it turns things.

## Sources

- OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ; Examples 10.14 and 10.15). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque (retrieved 2026-10-02)
- NIST SP 811 (2008), Appendix B.8, Factors for Units Listed Alphabetically (1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 in = 0.0254 m; 1 kgf = 9.80665 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-02)